@article{EJP200,
author = {Donald Dawson and Luis Gorostiza and Anton Wakolbinger},
title = {Hierarchical Equilibria of Branching Populations},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {9},
year = {2004},
keywords = {Multilevel branching, hierarchical mean-field limit, strong transience, genealogy},
abstract = {Abstract. The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group $\Omega_N$ consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium for this two-level branching system. In the limit $N\to\infty$ (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls $B^{(N)}_\ell$ of hierarchical radius $\ell$ converge to a backward Markov chain on $\mathbb{R_+}$. This limiting Markov chain can be explicitly represented in terms of a cascade of subordinators which in turn makes possible a description of the genealogy of the population.},
pages = {no. 12, 316-381},
issn = {1083-6489},
doi = {10.1214/EJP.v9-200},
url = {http://ejp.ejpecp.org/article/view/200}}